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This is an accepted version of this page This is the latest accepted revision, reviewed on 17 December 2024. Observation that in many real-life datasets, the leading digit is likely to be small For the unrelated adage, see Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of ...
Benford's law is an observation that in many real-life sets of numerical data, the leading digit is likely to be small. [21] In sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time.
Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.
Hill discovered what many consider to be the definitive proof of Benford's law. [1] [2] He is also known for his research in the theories of optimal stopping (including secretary problems and prophet inequality problems) and of fair division, in particular the Hill-Beck land division problem.
Benford's law. Benford's law. This was first stated in 1881 by Simon Newcomb, [1] and rediscovered in 1938 by Frank Benford. [2] The first rigorous formulation and proof seems to be due to Ted Hill in 1988.; [3] see also the contribution by Persi Diaconis. [4] Bertrand's ballot theorem.
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For example, a ranked list of US metropolitan populations also follow Zipf's law, [8] and even forgetting follows Zipf's law. [9] This act of summarizing several natural data patterns with simple rules is a defining characteristic of these "empirical statistical laws".
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